Question 12111
The answer in your book is wrong.  If you were to plug in {{{6/19}}} for the variable y, you would end up with an inequality.  The outcome would be 9=2{{{1/2}}}, which is false.  



Here is the solution:
{{{2/y}}}+{{{5/2}}}=4-{{{2/3y}}}


{{{2/y}}}+2{{{1/2}}}=4-{{{2/3y}}}            (((((subtract 2{{{1/2}}}from both sides


({{{2/y}}}+2{{{1/2}}})-2{{{1/2}}}=(4-{{{2/3y}}})-2{{{1/2}}}


{{{2/y}}}=(4-{{{2/3y}}})-2{{{1/2}}}


{{{2/y}}}=1{{{1/2}}}-{{{2/3y}}}             (((add {{{2/3y}}} to both sides


{{{2/y}}}+{{{2/3y}}}=1{{{1/2}}}-{{{2/3y}}}+{{{2/3y}}}


{{{2/y}}}+{{{2/3y}}}=1{{{1/2}}}           


multiply {{{2/y}}}by {{{3/3}}}


({{{2/y}}})({{{3/3}}})+{{{2/3y}}}=1{{{1/2}}}    


{{{6/3y}}}+{{{2/3y}}}=1{{{1/2}}}  


{{{8/3y}}}=1 {{{1/2}}} or {{{3/2}}}


{{{8/3y}}}={{{3/2}}}                  ((((((multiply both sides by {{{3y/8}}}


({{{8/3y}}})({{{3y/8}}})=({{{3/2}}})({{{3y/8}}}) 


1=9y/16                  ((((((((multiply both sides by {{{16/9}}}


{{{16/9}}}1=9y/16 {{{16/9}}}


{{{16/9}}}=y






....if you were to check your work, plugging in {{{16/9}}} for the variable y, you'd get 3{{{5/8}}}=3{{{5/8}}}which is correct.